Colin is buying dirt to fill a garden bed that is a 9 ft by 16 ft rectangle. If he wants to fill it to a depth of 4 in., how many cubic yards of dirt does he need?
If dirt costs $25 per yd3, how much will the project cost? (Hint: 1 yd3 = 27 ft3)
in feet, the dirt is
(9)(16)(1/3) = 48 ft^3
so, just divide that by 27 and multiply by the cost per cubic yard of dirt.
To calculate the volume of dirt needed, we can multiply the length, width, and depth of the garden bed.
1. Convert the depth from inches to feet:
Depth in feet = 4 inches / 12 inches/foot = 0.33 feet
2. Calculate the volume of the garden bed:
Volume = Length x Width x Depth
Volume = 9 ft x 16 ft x 0.33 ft = 47.52 ft³
3. Convert the volume from cubic feet to cubic yards:
Volume in cubic yards = Volume in cubic feet / 27
Volume in cubic yards = 47.52 ft³ / 27 = 1.76 yd³ (rounded to the nearest hundredth)
4. Calculate the total cost:
The cost per cubic yard is $25.
Total cost = Volume in cubic yards x Cost per cubic yard
Total cost = 1.76 yd³ x $25/yd³ = $44 (rounded to the nearest dollar)
Therefore, Colin needs approximately 1.76 cubic yards of dirt, and the project will cost around $44.
To find the volume of dirt Colin needs, we can use the formula: volume = length * width * depth.
1. First, let's convert the dimensions of the garden bed from feet to inches. Since 1 ft = 12 in, the dimensions will be: 9 ft * 12 in = 108 in and 16 ft * 12 in = 192 in.
2. Next, convert the depth of 4 inches to feet. Since 1 ft = 12 in, the depth will be: 4 in / 12 = 0.33 ft (approximately).
3. Now, we can use the formula to calculate the volume: volume = 108 in * 192 in * 0.33 ft.
4. To convert the volume from cubic inches to cubic yards, we need to convert from inches to yards. Since 1 yd = 36 in, we divide the volume by 46656 (36 * 36 * 36) to get the volume in cubic yards.
So, the volume of dirt Colin needs is approximately: 108 in * 192 in * 0.33 ft / 46656 = 6.39 cubic yards (rounded to two decimal places).
To find the cost of the project, we multiply the volume of dirt by the cost per cubic yard. In this case, the cost is $25 per cubic yard.
Therefore, the cost of the project will be approximately: 6.39 cubic yards * $25/yard = $159.75.